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marissa [1.9K]
3 years ago
5

Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If

100 women are randomly selected, find the probability that they have a mean height greater than 63.0 inches.

Mathematics
1 answer:
vesna_86 [32]3 years ago
6 0

Answer:

<h2>The probability is 58 %.</h2>

Step-by-step explanation:

This problem belong to a normal distribution probability.

Mean = 63.6

Standard Deviation = 2.5.

We have to find the probability of a height greater than 63.0.

Due to the normal probability, we need to find the Z score first:

Z=\frac{x-u}{o}; where x is the height, u is the mean, and o is the standard deviation.

Z=\frac{63-63.6}{2.5} \\Z= -0.24

Once we have our Z score, we find the probability with the z-table (attached). So, for a z score of -0.24 we have a probability of 0.42.

But, the problem is asking for height greater than 63.0, this mean that we have to subtract 0.42 from 1, giving as result 0.58, which means a 58% of probability,

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Step-by-step explanation:

<u>Step 1: Define equation</u>

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<u>Step 2: Solve for </u><em><u>x</u></em>

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<u>Step 3: Check</u>

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  1. Substitute:                    4(1/3) + 1 = 3 - 2(1/3)
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Step-by-step explanation:

Step 1

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The second step is to calculate the probabilities by multiplying the probabilities with the first 3 terms in the product being the probability of a win and the last term being the probability of a loss.

The calculation is shown below,

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The next step is to round down the percentage . The value of 6.25% rounded down is 6%. The correct answer is 6%.


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